Fiber-optic sensor and method

ABSTRACT

A fiber optic sensor and related method are described, with the sensor including a cross-coupling element in the optical path between a polarizing element and a sensing element, but separated from the sensing element itself; with the cross-coupling element generating a defined cross-coupling between the two orthogonal polarization states of the fundamental mode of a polarization maintaining fiber guiding light from the light source to the sensing element thus introducing a wavelength-dependent or temperature-dependent sensor signal shift to balance wavelength-dependent or temperature-dependent signal shifts due to other elements of the sensor, particularly signal shifts due to the wavelength dependence of the Faraday effect or the electro-optic effect constant.

FIELD OF THE INVENTION

The invention relates to a fiber optical sensor such as a fiber-opticcurrent sensor (FOCS) or magnetic field sensor that includes a sensingfiber to be exposed to a magnetic field, e.g. of a current to bemeasured, or such as a fiber-optic voltage sensor, both typically usedin high voltage or high current applications.

BACKGROUND OF THE INVENTION

Fiber-optic current sensors rely on the magneto-optic Faraday effect inan optical fiber that is coiled around the current conductor. Thecurrent-induced magnetic field generates a circular birefringence in theoptical fiber that is proportional to the applied magnetic field. Apreferred arrangement employs a reflector at the sensing fiber's far endso that the light coupled into the fiber performs a round trip in thefiber coil. Commonly, left and right circularly polarized light waves,which are generated from two orthogonal linearly polarized light wavesby a fiber-optic phase retarder spliced to the sensing fiber and actingas quarter-wave retarder (QWR), are injected into the sensing fiber asdescribed in the references [1-4]. After the round trip through thefiber coil the two circular waves have accumulated a phase delayproportional to the applied current as a result of the circularbirefringence in the fiber. This phase delay is proportional to thenumber of fiber windings around the current conductor, the appliedelectrical current, and the Verdet constant V(T, A) of the fiber. TheVerdet constant is thereby material-, temperature-, andwavelength-dependent.

As an alternative, the sensor may be designed as a Sagnac-typeinterferometer with quarter-wave retarders (QWRs) at both sensing fiberends and light waves of the same sense of circular polarization that arecounter-propagating in the sensing fiber.

In references [3, 5, 6] methods are disclosed where the fiber retarderis employed to balance the temperature dependence of the Verdetconstant, which is (1/V) dV/dT=0.7×10-4° C.⁻¹ for fused silica fiber.For this purpose, the retardance of the QWR is set to an appropriatelychosen value that commonly deviates from perfect quarter-waveretardance. The variation of the retardance with temperature changes thesensor scale factor such that it balances the variation of the Verdetconstant with temperature. A method how to manufacture such retarders isdisclosed in reference [7].

Typically, fiber-optic current sensors employ semiconductor lightsources such as superluminescent diodes (SLDs). If the source is nottemperature stabilized, its emission spectrum shifts to smallerwavelengths at increasing ambient temperature. Typical SLD wavelengthshifts correspond to a few tenths of a nanometer per ° C. depending ondetails of the SLD material system. The Verdet constant for fused silicafiber roughly scales with wavelength as V(λ)=V(λ₀)(λ₀/ λ)², as statedfor example in references [8, 9]. Here, λ₀ is the initial wavelength(reference wavelength). The relative scale factor variation at 1310 nmis thus −0.15%/nm or −0.05%/° C., if one assumes a wavelength shift withtemperature of 0.3 nm/° C. Apart from the Verdet constant, other sensorparameters may also change with source wavelength, for example theretardance of the fiber retarder at the beginning of the sensing fiber,and may thus influence the scale factor. The source wavelength alsovaries with drive current or may shift as a result of source aging.

To counter the shift in wavelength it is known to stabilize thewavelength of light source by operating the source at constant currentand stabilizing the source temperature by means of a thermoelectriccooler (TEC) or by monitoring the source temperature and appropriatelycorrecting the sensor signal. Wavelength shifts due to source aging arenot corrected when using these methods.

In the field of fiber-optic gyroscopes, several methods have beenreported to track wavelengths shifts in gyroscopes, including the use ofa tracking interferometer [10], wavelength division multiplexers[11-13], or fiber gratings [12, 14].

Further known are voltage or electric field sensors based on the Pockelseffect or linear electrooptic effect or on the use of an optical fibercoupled to a piezo-electric material. In these sensors, birefringenceinduced by the electric field or by force or anisotropic change in therefractive index of the material is used in the fiber optic sensor tomeasure voltages, electric field strength or force.

As discussed above, references [3, 5, 6] disclose how to compensate atemperature dependence of a fiber-optic current sensor. Hereby,generally, a first-order, i.e. linear, temperature-dependentcontribution that e.g. originates from the temperature dependence of theVerdet constant (dV/[VdT]=0.7×10⁻⁴° C.⁻¹ in fused silica fiber at 1310nm) is counteracted by a temperature-dependent behaviour of a fiberretarder at the entrance to the sensing fiber. WO 2014/154299 furtherdiscloses how to compensate a temperature dependent signal thatoriginates from a combination of the temperature dependence of theVerdet constant and the birefringence of the sensing fiber. However,these methods generally do not compensate a potential higher order, inparticular second order, i.e. parabolic or quadratic, temperaturedependence or can even introduce an additional higher order temperaturedependence. Depending on the detection method of the sensor (detectionwith non-reciprocal phase modulation or detection with passive phasebias), the curvature of the parabolic contribution can either bepositive or negative. A non-linear contribution can also originate frompolarization cross-coupling due to packaging-related fiber stress atextreme temperatures or temperature-dependent shifts of the optimumsensor working point, as e.g. shown in WO 2014/006121. U.S. Pat. No.5,696,858 discloses a fiber-optic sensor according to theprecharacterizing clause of the independent claims.

It is an object of the invention to provide a fiber optic sensor,particularly a magnetic field sensor or current sensor that includes asensing fiber to be exposed to a magnetic field, where the sensor signalis less sensitive to wavelength shifts of the light used and/or totemperature shifts.

SUMMARY OF THE INVENTION

Hence, according to a first aspect of the invention, a fiber opticsensor is provided including a light source, a polarizing element, adetector, a polarization maintaining (PM) fiber, and a sensing element,with the sensor further including a cross-coupling element in theoptical path between the polarizing element and the sensing element butnot directly connected to the sensing element, with the cross-couplingelement generating a defined cross-coupling between the two orthogonalpolarization states of the fundamental mode of the PM fiber.

The sensor can be a magnetic field or current sensor, in which case thesensing element is preferably a sensing fiber to be looped around aconductor and in operation exposed to a magnetic field of the current inthe conductor. Alternatively, the sensor can be an electric field orvoltage sensor, in which case the sensing element is preferably anelectro-optical crystal or a fiber force-coupled to a piezo-electricelement. For force or strain measurements the fiber can be directlycoupled to the object exerting the force or the strained object.

The polarizing element can be a light source inherently generating lightwith the desired polarization or it can be a part of the sensor separatefrom the light source such as a polarizing fiber, a polarizing beamsplitter, (fiber-coupled) bulk optic polarizer, a polarizing waveguide,such as a lithium niobate (LiNbO₃) waveguide made by proton exchange,and combinations thereof.

In general, the cross-coupling element can be introduced into theoptical path at any point in which it can provide the cross-couplingeffect between the two polarization states of the PM fiber. However, itis preferred not to locate the element too closely to the entry point ofthe light into the sensing fiber. In particular, the cross-coupling isnot directly attached to the sensing element, but best is separated fromit at least by a section of PM fiber and/or by at least by a retarderand/or by a Faraday rotator, i.e. is separated by at least one elementselected from the group consisting of: at least a section of PM fiber, aretarder, a Faraday rotator, and combinations thereof.

It is preferred to introduce the cross-coupling element into the opticalcircuit at a location closer to the proximate end of the PM fiber thanits distal end. If the sensor includes further active or passiveelements to modulate or bias the phases of the light before it enters adetector, such as optical modulators or passive phase retarders, it isparticularly preferred to have the cross-coupling element in proximityto these further active or passive elements.

Most preferably, the cross-coupling element is integrated between twosections of the PM fiber or, where present in the sensor, directlyattached to or integrated within an optical beam splitter elementlocated in the light path between the light source and the PM fiber.

The cross-coupling element is a separate element present in addition tothe PM fiber, in particular in addition to a non-ideal PM fiber havingresidual cross-coupling between orthogonal polarizations. In otherwords, the cross-coupling element introduces deliberate specific crosscoupling between the orthogonal light polarizations propagating into thePM fiber. Such purposeful cross coupling can add to practically presentcross-coupling in the optical circuit that results from non-idealoptical elements, such as PM fibers, polarizers, splices, retarders,modulators, etc.

In embodiments, the cross-coupling element introduces a wavelengthdependent part in the sensor signal that can be tuned such that shiftsin the sensor signal, in particular in its scale factor, introduced bythe wavelength dependent cross-coupling balance other changes in thesensor signal caused by shifts of the center wavelength λ of the light,in particular a change in the Verdet constant of the sensing element.

The cross-coupling element can be implemented in form of a non-exacthalf-wavelength retarder. The (non-exact) half-wavelength retarderintroduces a phase shift of m·180°+β(λ) between the two polarizationstates of the PM fiber, wherein m is an integer including zero and β(λ)is not zero and selected such that a shift of the center wavelength λaway from its initial value Xodoes not affect the signal as measured.

Often, it is particularly preferred to have further active or passiveelements, such as optical modulators or beam splitters, and in somevariants also the light source and or/the detectors, together with thecross-coupling element at the same location. In high voltage environmenta location on ground potential is often preferred. Thus, it is possibleto house both the further active or passive elements, such as opticalmodulators or beam splitters and in some variants also the light sourceand or/the detectors, and the cross-coupling element in a singlehousing, or at least sharing the same electrical supply line, so as tofacilitate having a controlled temperature environment to reduceinfluence of temperature on the cross-coupling element, even if thecross-coupling element has its own temperature controlled housingseparated from the other active or passive elements.

Alternatively or in addition to such external temperature stabilization,the coupling element can be stabilized inherently against temperaturefluctuations, e.g. by detuning of an additional retarder in the opticalpath, particularly a retarder located at the entry to the sensingelement, or by using several parts in the cross-coupling element withmutually counter-acting temperature dependences.

In embodiments of the sensor or method, the cross-coupling element is ahalf wave retarder with principal axes forming an orientation angle ζ ina range of ±15° or in a range of 90°±15° with respect to the principalaxes of the PM fiber, and with a half wave retardance δ(T₀,λ₀) equal toan integer multiple of 180° within ±20° to achieve a sensor signalinsensitive to temperature up to second order within a given temperaturerange.

In embodiments of the sensor or method, a retarder is adjusted tocompensate for linearly temperature-dependent shifts in the sensorsignal caused by temperature changes of any of the elements selectedfrom the group consisting of: the cross-coupling element, the sensingelement, further optical elements in the sensor; in particular whereinthe retarder introduces a quadratically temperature-dependent shift inthe sensor signal.

In embodiments of the sensor or method, a quadraticallytemperature-dependent contribution from the cross-coupling element tothe sensor signal counteracts a quadratically temperature-dependentcontribution from other elements, in particular from the retarder, tothe sensor signal.

Though other types of fiber-optic sensors using for example aSagnac-type configuration can be adapted to include elements of thepresent invention in case of it being a current sensor, it is preferredthat such a current sensor is of the reflective type. The sensingelement or fiber in such a sensor is terminated with a reflectiveelement, such as a reflector or a Faraday rotator mirror.

Due to the improved stabilization against shifts in the nominalwavelength λ of the novel sensor, the light source used can be of anon-temperature-stabilized type. Such light sources typically lack anactive heating or cooling element in close proximity of the lightemitting element, i.e. integrated into the so-called packaging of thelight emitting element.

Sensors in accordance with the invention are of particular use in thefield of measurements in a high-voltage environment (e.g. in the rangeof 72 kV to 800 kV) in power transmission networks, where accuratemeasurement, long lifetimes and robustness in widely varyingenvironmental conditions are required.

Further aspects of the invention include a method of measuring acurrent, a magnetic field, a voltage, an electrical field, a force fieldor a strain field using a fiber-optic sensor and introducing awavelength dependent shift of the signal by tuning a cross-couplingbetween the two polarization states of a PM fiber with thecross-coupling element introduced into the optical path between apolarizing element for the injected light and the sensing element of thesensor or between the polarizing element and any optical elementslocated at the entry point of the sensing fiber and directly attached toit.

In the method: the amount of tuning is selected such thatwavelength-dependent shifts in the sensor signal introduced by thecross-coupling balance other wavelength-dependent shifts in a measuredsignal as caused by shifts of the centre wavelength of the light. Suchshifts can include wavelength dependent shifts in the Verdet constant orin other optical elements, such as retarders and the like, of thesensor; and/or in the method the amount of tuning is selected such thattemperature-dependent shifts in the sensor signal introduced by thecross-coupling balance other temperature-dependent shifts in a measuredsignal. Such shifts can include or can be linearly and/or quadraticallytemperature-dependent shifts from the quarterwave retarder or from otheroptical elements (i.e. different from the cross-coupling element) of thesensor.

In embodiments, the cross-coupling element located in the optical pathbetween the polarizing element and the sensing element is used tobalance signal shifts introduced by a quadratic temperature dependencedue to other sensor elements by such shifts in the sensor signal thatare introduced by a quadratic temperature dependence of thecross-coupling element. In alternative or additional embodiments, thecross-coupling element located in the optical path between thepolarizing element and the sensing element is used to balance signalshifts introduced by a linear temperature dependence due to other sensorelements by such shifts in the sensor signal that are introduced by alinear temperature dependence of the cross-coupling element.

In embodiments, the cross-coupling element for balancingwavelength-dependent shifts and the cross-coupling element for balancingtemperature-dependent shifts can be the same or can be differentcross-coupling elements.

Even more preferably, the tuning of the cross-coupling between the twopolarization states of the PM fiber includes the step of introducing aphase shift of m·180°+β(λ₀) between the two polarization states, whereinm is an integer including zero and β(λ₀) is not zero and is selected tobalance wavelength-dependent shifts in a measured signal.

Another aspect of the invention is a fiber-optic sensor voltage orelectric field sensor with at least a light source and at least twolight detectors, at least three optical transmission channels, with onechannel providing a forward channel for the light to a sensing elementand two channels providing return detector channels for the light to thedetectors, and an integrated optical polarization splitter module forintroducing a static bias optical phase shift between two different setsof light waves, having different velocities within said sensing elementin the presence of a non-vanishing measurand field and for converting atotal optical phase shift including the static bias optical phase shiftand an optical phase shift induced by the measurand field into opticalpower changes of opposite signs (anti-phase) in the at least twodetector channels, and a polarization maintaining (PM) fiber with the PMfiber being connected directly or indirectly via at least one retarderor Faraday rotator element to the sensing element.

The two different sets of light waves can be for example orthogonallinear polarization modes or left and right circular polarization modes.Preferably, such a sensor includes a cross-coupling element forwavelength stabilization as described above.

For optical magnetic field sensors or current sensors according to thisinvention, the sensing element can comprise optical fibers orwaveguides, including specialty low birefringent fibers, flint glassfibers, or spun highly-birefringent fibers, bulk magneto-opticmaterials, such as yttrium iron garnet crystals or fused silica glassblocks, or optical fibers, waveguides, or bulk optical materialsattached to a magneto-strictive element [31], or combinations thereof.

For voltage or electrical field measurements according to thisinvention, the sensing element can comprise an electro-optical crystal,a crystalline electro-optic fiber (see ref. [24]), a poled fiber [25],or a fiber or bulk optic material attached to a piezo-electric element[32]. For force or strain measurements according to this invention, thesensing element can comprise an optical fiber or a bulk optic material.

A further aspect of the disclosed device (as already mentioned above forthe method), that can be used as addition or alternative to the previousaspects, is a compensation of a quadratic temperature dependence and/orof a residual linear temperature dependence in fiber-optic sensors, inparticular fiber-optic current sensors. Equally, this invention appliesto fiber-optic strain or voltage sensors. To this end, a cross-couplingelement is inserted into the optical circuit of a fiber-optical sensoras described with respect to other aspects of the disclosed invention:The cross-coupling element is placed between a polarizing element andthe sensing element, e.g. between two sections of polarizationmaintaining fiber, but is not directly coupled to the sensing element.The polarizing element can be selected from the range of choices asdescribed with respect to other aspects of the disclosed invention.Equally, the cross coupling element is preferably separated from thesensing element by at least a section of PM fiber, a retarder (inparticular a fiber retarder), a Faraday rotator, or a combination ofsuch elements. To expose the introduced cross-coupling element to asimilar or the same temperature as the sensing element and an optionalfiber retarder attached to the sensing element, the cross-couplingelement is preferably in spatial proximity to the sensing element andthe optional fiber retarder. In embodiments, the cross-coupling element,the sensing element and the fiber can retarder share a common housing.

The cross-coupling element adds a temperature dependent signal componentdue to temperature dependent cross-coupling between the two orthogonallinearly polarized light states of the polarization-maintaining fiber,whose temperature dependence counteracts the residual combinedtemperature dependence of the sensing element, an optional fiberretarder or Faraday rotator, and, if applicable, further components inthe optical path. Hereby, preferably, in the case of fiber-optic currentsensors, the parameters of the fiber retarder are chosen such that thelinear terms in the temperature dependence of the sensing element andthe retarder cancel each other, e.g. in a range from −40° C. to 85° C.,while a higher-order temperature dependence remains.

However, in this further aspect of the invention, the temperaturedependent contribution of the cross-coupling element is chosen tocompensate the residual parabolic or quadratic temperature dependence.

In other cases, the cross-coupling element can counteract a combinationof residual quadratic and linear temperature dependence of the signal.In general, the temperature dependent variation of the signalto-be-compensated can e.g. originate from the temperature dependence ofmechanical stress exerted on the sensing element, of bend-inducedbirefringence in a sensing fiber, of the magneto-optic or electro-opticeffect of the sensing element, of the piezo-electric effect of apiezo-electric material attached to the sensing element, of theintrinsic birefringence in the sensing element such as in a spunhighly-birefringent optical fiber, of the working point of the sensor,of a retarder or a Faraday rotator in the optical path, or ofcombinations thereof.

The cross-coupling element can be implemented in form of an exact ornon-exact half-wave retarder, i.e. with a retardation δ(T,λ) withT=temperature and λ=wavelength. In an embodiment, the retardation is setto δ(T₀,λ₀)=m·180°, with m being an odd integer number, T₀ being areference temperature, typically in the middle of the operatingtemperature range, and λ₀ being the mean operating wavelength. In thisembodiment, the principal axes of the retarder are oriented under 0°+ζor 90°+ζ with respect to the incoming light polarizations, e.g. given bythe principal axes of a polarization maintaining fiber link into whichthe cross-coupling element 16 is inserted. The orientation angle ζ andinteger m are then adjusted to compensate a quadratic temperaturedependence, introduced by other components of the optical circuit of thefiber-optical current sensor. This adjustment of m and ζ is chosen as afunction of the variation of retardance δ(T₀,λ₀) with temperature and ofthe amount of quadratic temperature dependence to be compensated for.

Please note that in general throughout this application, the half waveretardance δ(T₀,λ₀)=m·180°+β(m=0, 1 , 2, 3, . . . ) with β being thedeviation or detuning of the non-exact half wave retardance from theexact half wave retardance of multiple orders m of 180°.

In another aspect of the disclosed invention, two cross-couplingelements can be included in the optical path of the fiber-optic sensor(not shown). A first cross-coupling element can be used for compensationof the wavelength dependence of the sensor signal, while a secondcross-coupling element can be introduced to compensate a residualtemperature dependence of the sensor signal, in particular a quadratictemperature dependence. The first cross-coupling element is preferablydesigned as disclosed in the primary aspect of the invention, while thesecond cross-coupling element is designed as described in the otherinventive aspect of quadratic temperature dependence compensation. Inembodiments, the first cross-coupling element resides in a commonhousing with the opto-electronic module or with at least parts of theopto-electronic module, while the second cross-coupling element residesin a common housing with the sensing element.

The above and other aspects of the present invention together withfurther advantageous embodiments and applications of the invention aredescribed in further details in the following description and figures.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a schematic diagram of a fiber optic sensor head connected toa PM fiber of a sensor in accordance with an example of the invention;

FIG. 2A illustrates a cross-coupling by using a non-exacthalf-wavelength fiber retarder in a PM fiber;

FIG. 2B illustrates the function of a cross-coupling element;

FIGS. 3A and 3B illustrate examples of the invention as used in sensorsof a reflective type with active phase modulation for signal detection;

FIG. 4 is a numerical example of balancing signals shift due to shiftsin the center wavelength of light by means of a polarizationcross-coupling element;

FIG. 5 is an example of the invention as used in sensors of a reflectivetype with passive optical elements for signal detection;

FIG. 6 is another example of the invention as used in sensors of areflective type with passive optical elements for signal detection and aFaraday rotator mirror as terminal of the sensing element;

FIG. 7 shows an example of a temperature-insensitive cross-couplingelement;

FIG. 8 shows a cross-coupling element based on a Faraday rotator;

FIGS. 9A and 9B illustrate a fiber-optic voltage sensor in accordancewith two examples of the invention having an active phase modulationdetection scheme and a detection scheme with passive (static) phasebias, respectively;

FIG. 10 shows a typical normalized sensor signal versus temperature of astate-of-the-art fiber-optic current sensor;

FIG. 11 shows a fiber retarder as an embodiment of the cross-couplingelement; and

FIG. 12 shows a calculated normalized sensor signal of a fiber-opticcurrent sensor versus the temperature of the cross-coupling element(solid curve) and versus the common temperature of the sensing elementand a fiber retarder at the entrance to the sensing fiber (dashed curve)as well as the combined temperature dependence (dotted curve).

DETAILED DESCRIPTION

In FIG. 1 there is shown a general example of the present inventionillustrating configurations of the sensor head 10-1 of a reflectivefiber-optic current sensor 10 in a schematic manner. In this generalexample, a polarization maintaining (PM) fiber lead 11 transfers thelight into and back from the sensor head which includes a sensingelement 12 being in this example a sensing fiber 12 wound in one or more(N) loops around a conductor 13. Depending on the method of measuringthe magneto-optic phase shift, either a superposition of light in bothof the two orthogonal polarization states of the fundamental PM fibermode or only light in one polarization state is injected into thesensing fiber element 12.

Depending on the specific detection technique the linearly polarizedlight waves may be converted to circular waves before they enter thesensing fiber by using a retarder 14, which in the present example is afiber-optic QWR (quarter-wave retarder), located at the transition fromthe PM fiber 11 to the sensing fiber 12. A reflector 15 terminates thesensing fiber 12 at one end. The reflector 15 can for example be astandard mirror (e.g. a reflective coating 15 on the fiber tip) or aFaraday rotator mirror 15′. In certain sensors with rotator mirrors, theretarder 14 is omitted or implemented as a (detuned) half-wavelengthretarder.

In case where the sensor is a voltage sensor 90, the sensor head 10-1 asshown can be replaced by a different sensor head, in which the sensingfiber is replaced as the sensing element 12 for example by anelectro-optic crystal to measure a voltage ΔV applied over the length ofthe crystal, as detailed in FIG. 9 below.

If a temperature compensation of the sensor 10 is desired, the retarder14 can be detuned by an angle ε to (M·180°+90°+ε) in case of aquarter-wave retarder (or (M·180°+ε) in case of a half-wave retarder asdescribed for example in the references [3, 5, 6].

Also shown in FIG. 1 is an element 16 located in the example between twosections of the PM fiber 11. The element 16 is designed to cause adefined amount of cross-coupling between the two polarization states ofthe PM fiber 11.

In the context of the present invention the term “cross-coupling” meansthat light which has propagated in one polarization state of thefundamental mode, e.g. LP₀₁(x), before the cross-coupling element 16 issplit onto both states, LP₀₁(x) and LP₀₁(y).

It should be noted that this element 16 need not be located betweensections of the PM fiber 11 to achieve such a cross-coupling, butinstead can be located anywhere in the optical path between an initiallinear polarizer and the sensing element 12 (though not directly coupledto its proximate end), for example between the linear polarizer and PMfiber 11, or between PM fiber 11 and retarder 14. In embodiments where alight source generates directly light with the desired polarization,such as specifically designed laser, such a light source is understoodto include the initial polarizer.

Details of an example of the cross-coupling element 16 and its functionare illustrated in FIGS. 2A and 2B. In FIG. 2A the cross-couplingelement 16 is shown as a non-achromatic fiber-optic retarder integratedwithin the PM fiber 11. Below the illustration of the fiber 11, there isshown a graph indicating the relative orientation of fast and slow axesof the fiber retarder 16 with respect to the principal axes of the PMfiber 11. The orientation and in particular the length (i.e. thedifferential phase retardance between the orthogonal polarizationstates) of the retarder 16 is designed to cause a controlled amount ofpolarization cross-coupling (or mode mixing) between the two orthogonalpolarization states of the fundamental mode of the PM fiber 11, LP₀₁(x)and LP₀₁(y), as indicated in FIG. 2B for sensors using both orthogonalpolarization states (upper half of FIG. 2B) or sensors using only onepolarization state (lower half of FIG. 2B).

The cross-coupling changes the scale factor (or sensitivity) of thesensor 10 in a defined manner. Since the retardance of the retarder 16and thus the cross-coupling varies with wavelength, it can be used tocompensate for variations in the Verdet constant and other sensorparameters which change when drifts in the wavelength of the lightoccur. The phase retardance δ of the retarder 16 at the centerwavelength is set in this example to m·180°+β(m=0, 1, 2, 3, . . . ),with m=0 being a possible choice when β>0.

It should be noted that if the retarder 16 were an exact zero-order ormultiple order half-wave retarder (i.e. β=0) there would be noadditional cross coupling between the orthogonal modes of the PM fiberlead. As the retardance achieved with the cross-coupling element 16varies with the actual wavelength in a known manner, β can be set tocompensate for a change in the sensor signal, in particular of its scalefactor, due to the change of the Verdet constant with wavelength. Themethod can also compensate the wavelength dependence of other elementsin the optical path, in particular of the retarder 14 at the entrance tothe sensing fiber 12 as shown in FIG. 1 above.

The compensation of the wavelength dependence as described above can beintegrated in all fiber-optic current sensor configurations, in which aPM fiber lead transfers the light to the sensing fiber and/or from thesensing fiber. In the reflective sensor configurations of FIG. 1 thecross-coupling occurs both during the forward and return travel of thelight.

In the following, there is shown in greater detail, how thecross-coupling element 16 can be integrated into three distinct sensorconfigurations: a fiber-optic current sensor with non-reciprocal phasemodulation for phase biasing (illustrated in FIGS. 3), a fiber-opticcurrent sensor with a quarter-wave retarder for passive phase biasing(FIG. 5), and a fiber-optic current sensor with a Faraday rotationmirror for passive phase biasing (FIG. 6).

These designs differ in how the magneto-optical birefringence in thesensing fiber is detected and with the cross coupling element 16 beingadapted accordingly.

In a fiber-optic current sensor design with non-reciprocal phasemodulation, as shown in FIG. 3A, light is injected, preferably from alow coherent light source 1 such as a superluminescent diode, afterpassing through an optical fiber, a fiber coupler 101 and an initialoptical fiber polarizer 2, which reduces the emitted light into a singlelinear polarized state, injected at a 45° fiber splice 3 into bothorthogonal polarization states of the PM fiber 11, which in turn areprojected onto circular or close to circular light states in the sensingfiber 12 by a fiber-optic retarder 14. The two light states in thesensing fiber 12 acquire a magneto-optic phase delay due to the appliedelectrical current (Faraday effect). The phase delay is detected bymeans of a closed-loop detection circuit that includes an optical phasemodulator 4 and a detector 5 linked to the optical path by the fibercoupler 101. The optical phase modulator 4 and the detector 5 are alsoelectrically linked through a signal processor 6 for the closed loopdetection. Alternatively, an open-loop detection circuit may be used.

It should be understood that in these as in the following examplescomponents cited can be replaced by components with identical or similarfunctionality. For example, the light source 1 mentioned can be replacedby other types of light sources 1, such as light emitting diodes (LEDs),edge-emitting LEDs, vertical-cavity surface-emitting lasers (VCSELs),doped-fiber light sources, or laser diodes. Similarly, the modulator 4of FIG. 3A may be an integrated-optic birefringence modulator, such as alithium niobate modulator, or a piezoelectric modulator. The lattermodulates the differential phase of the orthogonal polarization statesby modulating the optical length of a section of PM fiber 11 that isattached to the modulator.

As described in the references cited, the quarter-wave retarder 14 canbe detuned from exact quarter-wave retardance by ε to achieve anintrinsic temperature compensation of the sensor (also a higher orderretarder can be used, such that the retardance ρ of the quarter-waveretarder amounts in total to ρ=M·180°+90°+ε where M=0, 1, 2, 3, . . . ), see for example references [3, 5, 6].

In the case of no birefringence in the sensing fiber 12 apart from themagneto-optic birefringence, the current signal at small magneto-opticphase shifts of sensors according to FIGS. 3A, 3B is in goodapproximation proportional to

S˜(−1)^(M)V(T, λ)NI/cos ε(T, λ)   [1]

Here, N is the number of loops of the sensing fiber coil 12, and I thecurrent in the conductor 13. A change in sign indicates a phase shift of180° between the current and the resulting signal. The Verdet constant Vgenerally varies linearly with temperature T and is a function ofwavelength λ. M and ε(T₀, λ) can be chosen so that the current signalbecomes independent of temperature, as done in the references mentionedabove. Here, T₀ is a reference temperature, e.g. room temperature.

In the prior art, the wavelength is commonly kept stable by working witha temperature-stabilized light source 1. If the wavelength shifts by Δλ(herein assuming Δλ/λ₀<<1), the relative signal change ΔS/S₀ (with S₀being a central or an undisturbed signal) is given by

ΔS/S ₀=(−2−tan ε(T, λ ₀)[M·180°+90°+ε(T, λ ₀)])Δλ/λ₀   [2]

wherein the first term, i.e. −2Δλ/λ₀, results from the wavelengthdependence of the Verdet constant V, and the second term results fromthe wavelength dependence of the retarder 14 when assuming that theretardance of the retarders 14 varies inversely proportional to thewavelength and that the Verdet constant of the sensing fiber 12 showsquadratic dispersion as previously reported, see ref. [8]. In case of adifferent type of dispersion, the principle of this calculation is notaltered, but the values given herein for β have to be adapted.

Eq. [2] has been derived from a description of the wave propagation inthe optical circuit by means of the Jones matrix formalism, which isshown in general form in reference [15]. As noted, in the referencescited above, M and ε(λ₀) are chosen so that the overall current signalbecomes nearly independent of temperature. For instance, with atemperature dependence of the Verdet constant of C_(Verdet)=0.7·10⁻⁴C°⁻¹ in fused silica fiber and assuming a temperature coefficient of theretarder of C_(QW)=−2.4·10⁻⁴ C° ⁻¹, a quarter-wave retarder having M=0and ε(λ₀)=9.5° results in an essentially (linearly) temperatureindependent signal. This sensor of prior art however still yields,according to eq. [2], a relative (combined) wavelength dependence ofΔS/S₀=(−2−0.29)Δλ/A₀=−2.29 Δλ/λ₀.

This wavelength dependence can be balanced in accordance with theexample shown by using a retarder as cross-coupling element 16 withretardance m·180°+β(λ) arranged in the optical path of the emitted lightafter the polarizer 2 but before the retarder 14. In the example, thecross-coupling retarder 16 is included in the opto-electronic module10-2 which comprises most components of the sensor 10 with the exceptionof the components of the sensor head 10-1 and parts of the PM fiber 11.The opto-electronic module 10-2 and the sensor head 10-1 are opticallyconnected through the PM fiber 11. The cross-coupling element 16 can bemaintained at constant temperature separately or inside a housing of theopto-electronics module 10-2.

The wavelength-dependence-compensating retarder 16 is essentially a zeroor multiple order half-wave retarder (HWR) with a phase deviation β(π)from perfect half-wave retardance. Using such a cross coupler 16 andassuming small magneto-optic phase shifts NVI (NVI<<1), the signal S isapproximately proportional to

S˜(−1)^(M+m) V(λ)NI/[cos ε(λ)cos β(λ)]  [3]

The relative change ΔS_(HWR) in sensor signal at a wavelength change Δλresulting from the extra retarder 16 can be written as

ΔS_(HWR) /S ₀=−tan β(λ₀)[m·180°+β(λ₀)]Δλ/λ₀   [4]

with λ₀ being the nominal center wavelength of the sensor 10 and inparticular S₀=S(λ₀). The integer m and the deviation or phase β(λ₀) fromperfect half-wave retardance can be adjusted so that the termΔS_(HWR)/S₀ of eq. [4] balances the term ΔS/S₀ of eq. [2], i.e. thecurrent signal becomes independent of wavelength.

For instance, m=2 and β(λ₀)≈−21° can be chosen to effectively compensatethe wavelength dependence of the Verdet constant and of the quarter-waveretarder 14. In the above derivation it is assumed that the temperatureof the compensating cross-coupling retarder 16 is kept constant or thatits retardance is essentially independent of temperature. As mentionedand described below in more details, this can be for example achieved byplacing the cross-coupling element 16 in a constant temperatureenvironment.

In embodiments, already β(λ₀)≈−20° or β(λ₀)>−20° (i.e. β(λ₀) being lessnegative than −20°) can effect a partial (yet useful) compensation ofthe wavelength dependence of the Verdet constant and of the quarter-waveretarder 14.

In a variant of these examples as shown in FIG. 3B, the phase modulator4 of the type as shown (birefringence modulator) may be replaced by ay-type integrated optic phase modulator 41 with PM fiber pig tails asoften used in fiber-optic gyroscopes and a polarization-maintainingfiber coupler 43 as described in more detail in references [19, 20]. Inthis example, the modulator 41 also acts as initial polarizer. The twolight waves with parallel polarization directions emerging from themodulator are projected onto the orthogonal linear polarization statesof the pm fiber 11 by a 90°—fiber splice 42 and by thepolarization-maintaining fiber coupler 43. The second arm of themodulator 41 includes an optical delay element 44.

The half-wave retarder 16 is then preferably arranged in the PM fiberlink 11 between the fiber coupler 43 and the sensing fiber coil 12.Alternatively, an appropriately adjusted half-wave retarder can beplaced into each of the two fiber arms between the y-modulator 41 andthe PM coupler 43.

In this example, the cross-coupling element is shown in atemperature-controlled housing 160 spatially separated from the othercomponents. This arrangement can be regarded as an alternative toincluding the cross-coupling element 16 in the opto-electronic module10-2.

In FIG. 4 there is shown the variation of sensor signal S vs. wavelengthof a compensated sensor together with the individual contributions fromVerdet constant S(V(λ)), the quarter wave retarder S(ε(λ)) and thecompensating cross-coupling retarder S(β(λ)). The signal variationwithout compensation (combined contribution from Verdet constant andquarter-wave retarder) corresponds to 3.5% for the wavelength span (20nm) in FIG. 4. The residual signal variation after compensation isnegligible.

In a fiber-optic current sensor design with splitter and with passivelygenerated phase bias as shown in FIG. 5, the same design for the sensorhead 10-1 is used as in the previous embodiments (e.g. FIG. 1). Insteadof closed-loop detection with an optical phase modulator 4, 41 as in theprevious example of FIG. 3, a detection scheme with a passivelygenerated phase bias is employed in this example, as described in detailin reference [16]. In such an arrangement, the sensor 10 includes againa light source 1 which preferentially generates non-polarised light toenter an optical path with an optical fiber, an initial linear polarizer55 a (in 45° orientation with respect to the axes of the PM fiber 11)attached via a spacer 53 made of glass to an integrated-optic splitter54. The light exits the integrated-optic splitter 54 via a PM fiber 11with a cross-coupling element 16. The light returning from sensing fiber12 is split and then passes a quarter-wave retarder and appropriatelyoriented polarizers 55 b, 55 c. The retarder 56 introduces a90°-phase-bias between the returning light waves. The light is guidedthrough two optical fibers to the respective detectors 5-1, 5-2, whichcan be photodiodes. The signals S_(1,2) at the two detectors 5-1 and 5-2are given by

S_(1,2)˜1±(−1)^(M) cos ε sin 4NVI   [5]

Dividing the difference of the two signals by their sum gives a signalthat is independent of the light source power and is proportional to

S˜(−1)^(M)V(T, λ)N I cos ε(T, λ)   [6]

Here, it is assumed that 4NVI<<1. The fiber quarter-wave retarder 14 atthe near end of the sensing fiber 12 is again used to achieve atemperature independent current signal, i.e. the retarder deviates by anappropriate amount ε from perfect quarter-wave retardance, see alsoreference [16]. It should be noted that the retarder 56 and spacer 53can also be interchanged such that the phase bias is introduced in frontof the sensor head 10-1.

As in the previously described embodiments, another fiber retarder 16 isinserted as cross-coupling element 16 in the PM fiber lead 11 of thesensing coil 12 to achieve a wavelength-independent current signal. Withthe introduction of the additional retarder 16 the current signal isapproximately proportional to (when again assuming that the sensingfiber is free of any non-magneto-optic birefringence)

S˜(−1)^(M+m)V(λ)N I cos ε(λ)cos β(λ)   [7]

Analogously to the previous case, β(λ₀) and N can be chosen such thatthe individual contributions to the overall wavelength dependence of thecurrent signal compensate each other. The retardance of the quarter-waveretarder can be set to M=0 and ε(λ₀)=−9.5° to balance the temperaturedependence of the Verdet constant (assuming that the sensing fiber isfree of linear birefringence). The relative wavelength dependence of thesensor signal amounts to

ΔS/S ₀=Δλ/λ₀(−2+[M·180°+ε(λ₀)] tan ε(λ₀)+[m·180°+β(λ₀)]tan β(λ₀))

In the given example, the half-wave retarder 16 can be set to N=2 andβ(λ₀)=21° to compensate the variations of the sensor signal withwavelength due to the combined contributions from the Verdet constantand the quarter-wave retarder: ΔS/S₀=(−2−0.29)Δλ/λ₀=−2.29 Δλ/λ₀. Notethat the absolute value of β(λ₀) is the same as for the sensor designswith non-reciprocal phase modulation (FIG. 3A, FIG. 3B) but the sign isopposite. With the values above, the individual signal contributions areagain as those shown in FIG. 4.

In embodiments, already β(λ₀)≈+20° or β(λ₀)<+20° (i.e. β(λ₀) beingsmaller than +20°) can effect a partial (yet useful) compensation of thewavelength dependence of the Verdet constant and of the quarter-waveretarder 14.

In another embodiment as illustrated in FIG. 6 the sensor coil 12 isterminated by a Faraday polarization rotator mirror 15′ for phasebiasing (see also references [17, 18] for further details). The Faradayrotator 15′ biases the current induced magneto-optical phase shift by90°, i.e. this rotator 15′ corresponds to a single pass polarizationrotation angle of 22.5° (or equivalently a single pass differentialphase shift of 45° for left and right circular light waves).

Hence, light from the light source 1 is guided through an optical fiberinto a combined polarizing splitter 24 and into the PM fiber 11 with anintegrated cross-coupling element 16. On the return after beingreflected and phase-shifted by the rotation mirror 15′, the signals atthe two detectors 5-1, 5-2 are equivalent to the signals in the previousconfiguration and are given by:

S_(1,2)˜[1±sin(4NVI+4α)].   [9]

The term α(T, λ) is the deviation of the single pass rotation angle ofthe Faraday rotator from 22.5°. Dividing the difference of the twosignals by their sum again gives a signal that is independent of thelight source power (with the assumption 4NVI<<1):

S˜V(T, λ)N I cos 4α(T, λ)   [10]

The half- or quarter-wave retarder 14 in some sensor designs between thePM fiber 11 and the sensing fiber 12 (see also FIG. 1) is set to zerofor the sake of simplicity (M=0 and s=0). By including an extra retarderas cross-coupling element 16 in the PM fiber link 11 to achieve thedisclosed controlled, wavelength-dependent polarization cross-coupling,the current signal is as well proportional to cos²β(λ). Properadjustment of N and β enables compensation of the wavelength dependenceof the current signal, including a compensation of the wavelengthdependence of the Faraday rotator 15′ and the sensing fiber 12.

The compensation for wavelength dependency is not limited to thewavelength-dependent contributions from the Verdet constant of thesensing fiber 12 and contributions from the retarder 14. It can alsocompensate other contributions, such as those of the embedded linearbirefringence in a spun, highly birefringent sensing fiber 12 or of thebend-induced linear birefringence in a sensing fiber 12 with lowintrinsic birefringence. Hence, the value of β has to be appropriatelyadapted, if the cross-coupling element 16 is also to compensate forthose elements.

In the above variants it was assumed that the cross-coupling element 16is kept at constant temperature by a temperature stabilizationenvironment 160. Particularly, in the sensor according to FIG. 3A orFIG. 3B, the extra retarder 16 is preferably part of the optoelectronicmodule 10-2. At this location, a stable temperature of thecross-coupling element 16 can be achieved, for example by means of athermoelectric cooler/heater (not shown).

In addition or alternatively, the temperature of the cross-couplingelement 16 can be measured and the temperature-dependence of thecross-coupling element 16 can be corrected at a signal processing stage.Small or negligible temperature dependence of the element 16 can also beachieved through the use of a fiber with low temperature dependence ofthe differential phase shift such as polarization-maintaining fiberswith birefringence determined by their geometrical structure, e.g.elliptical core or micro-structured fibers. Such fibers are known toshow a relatively weak temperature dependence in comparison to fiberswith stress induced birefringence.

A compensation of the temperature-dependence of element 16 can also beachieved, if both the cross-coupling element 16 in the PM fiber link andthe retarder 14 at the beginning of sensing fiber 12 are subject to thesame ambient temperature. In such a case the additional temperaturecontribution stemming from the cross-coupling element 16 can be balancedby an extra contribution from the retarder element 14 to the overalltemperature dependence of the signal. Taking again a configuration as inFIG. 3 as an example, the relative signal change due to a temperaturechange AT of the cross-coupling element 16 amounts to ΔS/S₀=tan β(T₀,λ₀)[N·180°+β(T₀,λ₀)] C_(HW) ΔT, wherein the constant C_(HW) describes therelative change of the retardance with temperature. Both retarders 14,16, i.e. m, M, s, and β, can be adjusted so that the overall temperaturedependence as well as the overall wavelength dependence vanishes. Inmore detail, the parameters have to be chosen so that not only dS/dλ=0(or small) is fulfilled (as in the examples above), but also dS/dT=0 (orsmall), which in the example of FIG. 3A results in:

0=−2−tan ε(T ₀,λ₀)[M·180°+90°+ε(T ₀,λ₀)]−tan β(T ₀,λ₀)[m·180°+β(T₀,λ₀)]  [11]

and

0=C _(Verdet) +C _(QW) tan ε(T ₀,λ₀)[M·180°+90°+ε(T ₀,λ₀)]+C _(HW) tanβ(T ₀,λ₀)[m·180°+β(T ₀,λ₀)]  [12]

As a further alternative or in addition to other thermal stabilizationmethods as described above, it is possible to prepare the cross-couplingelement 16 as an athermal retarder. This can be achieved as illustratedin FIG. 7. Here, the cross coupling element 16 consists of two sectionsof PM fiber: a fiber section 16-1 of length l₁ with small temperaturedependence (e.g. an elliptical-core fiber) and a section of length l₂with larger temperature dependence (e.g. a Panda fiber). The two fibersections 16-1, 16-2 are joined with a 90°—offset in the orientation oftheir principal axes. As a result the birefringent phase changes due totemperature changes add with opposite sign and tend to cancel eachother. Assuming for simplicity that the birefringence An (and beatlength) of both fiber sections is the same but the temperaturecoefficients differ by a factor of 5, the combined phase retardance ofthe two fiber sections will be independent of temperature if the lengthratio is chosen as: l₁:l₂=5:1. The length l₁ must be chosen as l₁=(5/4)λ₀φ/(2πΔn) in order to achieve the desired total retardance of φ atreference center wavelength λ₀.

It should be noted that the above described methods and components forreducing the temperature dependence of the sensor 10 can be usedseparately or in isolation from each other or in combination with eachother.

While only reflective sensor configurations are considered in the aboveexamples, the invention also applies to Sagnac-type fiber optic currentsensors, see for example reference [3] and other types of non-reflectivefiber-optic current sensors that contain a PM fiber lead to transmitlight from or to the sensing fiber. In a Sagnac-type current sensoraccording to reference [3], at least one appropriately adjustedcross-coupling element can be included into each of the PM fiber leadsof the sensor. As a result of the application of the half-waveretarders, part of the light travels with a polarization orthogonal tothe launched polarization direction in between the retarders. Thereby,the sensitivity of the sensor can be controlled in a wavelengthdependent manner, since the cross-coupled light experiences a Faradayphase shift of opposite sign.

In the detailed embodiments disclosed in this document, a 45° degreeangle between the axes of the PM fiber 11 and the axes of the retarder16 is assumed. It is preferred that the tolerances of this angle (i.e.orientation angle remain within ±(45°±10°) or at least within±(45°±22.5). However, it is to be understood that an angle differentfrom 45° can also be chosen intentionally. In this case the retardanceof cross-coupling element 16 must be adapted accordingly in order toachieve again full compensation of effects of source wavelength shiftson the sensor signal sensitivity.

In the examples shown, the cross-coupling retarder 16 is integratedbetween two parts of the PM fiber 11, which is in most cases thepreferred location. However, it is also possible to place thecross-coupling retarder 16 between the phase modulator 4 and the PMfiber 11, between the 45°-splice 3 and the phase modulator 4, or betweenbeam splitter 54 and the PM fiber 11 or even integrate it into the beamsplitter 54. On the other hand, it is possible to position thecross-coupling element 16 just before the components of the sensor head,e.g. between distal end of the PM fiber 11 and any additional retardersuch as retarder 14.

Depending on the sensor embodiment, the cross-coupling element ispreferred to be in a common housing with the phase modulator 4 or thebeam splitter 54.

In another embodiment as illustrated by FIG. 8, a Faraday rotator can beused as cross-coupling element 16. A Faraday rotator 16 comprises amagneto-optic crystal 161 and a permanent magnet 162 exerting a magneticfield on the crystal 161. A fiber-coupled Faraday rotator 16 typicallycomprises in addition lenses 163 to couple the light into and out of thePM fiber 11. The crystal 161 rotates incoming linear light polarizationstates by an angle defined by the type and length of the crystal 161 andby the magnetic field of the permanent magnet 162.

To achieve wavelength compensation, the Faraday rotator 16 can be setfor example to a single-pass rotation angle of i*90°+γ at the wavelengthλ₀, wherein i is any integer including zero and γ a bias rotation angle.Due to the wavelength dependence of the magneto-optic effect in thecrystal, γ is wavelength dependent, e.g. γ˜λ⁻². With γ≠0, this Faradayrotator 16 generates a wavelength dependent cross coupling between thetwo polarizations of the PM fiber as described previously. Accordingly,i and γ can be chosen to balance all wavelength dependent contributionsto the sensor signal similar to the case of retarder described in detailbefore.

The invention can also be used with sensors that work with orthogonallinear polarizations in the sensing medium rather than circularpolarizations and that employ detection schemes according to FIG. 3A, 3Band FIG. 5. Patent publication WO 2008/077255A1 (cited as reference[21]) discloses for example, how the detection schemes according toFIGS. 3A, 3B with active phase modulators can be adapted for sensingelements that work with orthogonal linear polarizations, see also Ref.[22, 23]. Even though not explicitly mentioned in Ref. [21], theadaptation is also valid for detection schemes with passive phasebiasing, such as described above with reference to FIG. 5.

As mentioned above when referring to FIG. 1, aspects of the inventioninclude the use of a cross-coupling element 16 in an optical voltage orelectric field sensor 90. A first example of such a sensor is shown inFIG. 9A. The general arrangement and rpeviously known components aredescribed in further detail for example in reference [21]. As in FIG.3A, the detection system includes a light source 1, a fiber coupler 101,a polarizer 2, a polarizer 3, an active phase modulator 4, a detector 5and a signal processor 6. Two light waves with orthogonal polarizationdirections are again injected in a PM fiber 11 and sent towards thesensing element 12. For voltage measurements, the sensing element 12 ofFIG. 9A includes a rod shaped electro-optic crystal 12, such as e.g. aBi₃Ge₄O₁₂ (BGO) crystal to measure a voltage applied over the length ofthe crystal 12. Instead of a bulk electro-optic crystal a crystallineelectro-optic fiber (e.g. also of Bi₃Ge₄O₁₂) [24] or an electricallypoled fiber, as described for example in reference [25], can be used, aswell.

A Faraday polarization rotator 14′ rotates the two orthogonal lightwaves emerging from PM fiber 11 by 45° before they enter theelectro-optic crystal 12. The polarization directions after the Faradayrotator 14′ coincide with the electro-optic axes of the crystal 12. Thelight is reflected at the far end of the crystal 12 by the reflector 15.The two orthogonal light waves experience a differential electro-opticphase shift in the crystal 12 that is proportional to the appliedvoltage. The Faraday rotator 14′ rotates the returning light waves byanother 45° so that the total roundtrip polarization rotationcorresponds to 90° like in the current sensor of FIG. 3A. (Thepolarization rotation is needed so that the roundtrip group delay of theorthogonal polarization states in PM fiber 11 is zero and the two wavesare again coherent when they interfere at the polarizer. Moreover, themodulation concept assumes swapped polarization states on the returnpath.)

The cross-coupling element 16 in the PM fiber is added again tocompensate for wavelengths shifts of the light source. Assuming thecross-coupling element 16 is a detuned half-wave retarder, and thedetuning angle or detuning phase shift β(λ_(o)) is now adjusted so thatthe cross-coupling element 16 balances the wavelength dependence of theelectro-optic effect. Other than the Faraday effect (Verdet constant)the electro-optic effect varies in proportion to the inverse of thewavelength (rather than the inverse of the square of the wavelength). Asa result the proper value of β(λ_(o)) in case of the electro-opticeffect is only half the value of β(λ_(o)) in case of the Faraday effect.Moreover, β(λ_(o)) can be chosen such that it compensates for thewavelength dependence of Faraday rotator 14′ (and possibly furthercomponents) in addition to compensation for the wavelength dependence ofthe electro-optic effect.

A second example of a voltage sensor 90 is shown in FIG. 9B. The sensingelement 12 includes a rod shaped electro-optic Bi₃Ge₄O₁₂ (BGO) crystal12 to measure a voltage applied over the length of the crystal 12.Instead of a bulk electro-optic crystal 12 an electro-optic fiber 12 maybe used such as a crystalline fiber [24] or an electrically poled fiber,as described for example in reference [25].

A Faraday polarization rotator 14′ rotates the two orthogonal lightwaves emerging from PM fiber 11 by 45° before they enter theelectro-optic crystal 12. The polarization directions after the Faradayrotator 14′ coincide with the electro-optic axes of the crystal 12. Thelight is reflected at the far end of the crystal 12 by means ofreflector 15. The two orthogonal light waves experience a differentialelectro-optic phase shift in the crystal 12 that is proportional to theapplied voltage. The Faraday rotator 14′ rotates the returning lightwaves by another 45° so that the total roundtrip polarization rotationcorresponds to 90°.

In the example of FIG. 9B a detection scheme with a passively generatedphase bias is employed, as described in detail in reference [16] andwith reference to FIG. 5 above. In such an arrangement, the sensor 90includes again a light source 1 which preferentially generatesnon-polarized light to enter an optical path with an optical fiber, aninitial linear polarizer 55 a (in 45° orientation with respect to theaxes of the PM fiber 11) attached via a spacer 53 made of glass to anintegrated-optic splitter 54. The light exits the integrated-opticsplitter 54 via a PM fiber 11 with an optional cross-coupling element16. The light returning from the sensor head 10-1 is split and thenpasses a quarter-wave retarder 56 and appropriately oriented polarizers55 b, 55 c. The retarder 56 introduces a 90°-phase-bias between thereturning light waves. The light is guided through two optical fibers tothe respective detectors 5-1, 5-2, which can be photodiodes. It shouldbe noted that the retarder 56 and spacer 53 can also be interchanged,i.e. with the spacer element in front of the polarizers 55 b and 55 csuch that the phase bias is introduced prior to entering the sensor head10-1. In the example of FIG. 9B the initial linear polarizer 55 a (in45° orientation with respect to the axes of the PM fiber 11) the spacer53, the 1×3 integrated-optic splitter 54, the quarter-wave retarder 56and the polarizers 55 b, 55 c are shown as an single integrated passiveoptical module, herein referred to as integrated optical polarizationsplitter module 50.

It should be further noted that the compensation provided by thecross-coupling element 16 is optional for operation of the sensor ofFIG. 9B. Hence in a variant of the example of FIG. 9B the cross-couplingelement 16 and its temperature stabilizing environment 160 can beomitted, in particular when the light source is itself temperaturestabilized.

There is a variety of options how to install a voltage sensor of thiskind in high voltage power transmission systems. In air-insulatedsubstations the sensing element may be mounted in an insulator with gas[26] or dry insulation [27]. The insulator may be installed as afree-standing insulator or hanging from a power line. In gas-insulatedswitchgear it may be installed in ways as disclosed in [28] and [29].Furthermore, the sensing element may be part of a capacitive voltagedivider and measure only a fraction of the line voltage [30]. It shouldbe noted that instead of the integrated-optic splitter (54) withwaveguides as shown in in FIGS. 5, 9B, a splitter of the samefunctionality can be made using bulk components, e.g. using beamsplitter cubes and/or prisms.

The method of the present invention can be applied for compensation ofwavelength shift also in other sensor configurations, for example thosedisclosed in Ref. [21]. In particular, the sensing element 12 mayrepresent an optical voltage sensor based on the piezo-electric effectin materials such as quartz. The quartz element(s) strain(s) a PMsensing fiber in the presence of an applied voltage and as a resultintroduce(s) again a voltage-dependent phase shift between theorthogonal polarization states of the sensing fiber (see ref. [21] forfurther details). The PM sensing fiber may also in a similar manner actas a sensor for strains or forces of other origin.

Note that the Faraday rotator 14′ of FIGS. 9 has a function differentfrom the Faraday rotator of FIG. 8, which acts as a cross-couplingelement 16 and different from the Faraday rotator 15′ of FIG. 6, whichacts as a phase biasing element.

The light source may already emit light with a sufficiently high degreeof linear polarization due to inherent polarization means or anintegrated polarizer. In this case, at least parts of the functionalityof the polarizers 2, 41, 55 a, 24 as shown in FIGS. 3A, 3B, 5, and 9 canbe incorporated into the light source. This requires all fibercomponents between source 1 and sensor element 12 to bepolarization-maintaining.

In the following, the further aspect of the invention is discussed indetail. For the fiber-optic current sensor configurations similar toFIGS. 3A, 3B but not including the shown cross-coupling element 16, thecurrent signal is in good approximation proportional to the expressiongiven in equation [1], with the two temperature dependent contributionsfrom V(T,λ) and s(T,λ). The linear temperature dependence results in arelative change ΔS/S₀ of the sensor signal (with S₀ being a central orundisturbed signal) given by equation [13]:

ΔS/S ₀ =ΔT·(C _(Verdet) +C _(QW) ·[M·180°+90°+ε(T ₀,λ₀)]·tan[ε(T ₀,λ₀)])  [13]

wherein ΔT=temperature change of the cross-coupling element 16,C_(verdet)=temperature dependence of the Verdet constant,C_(QW)=temperature coefficient of the retarder, M=0, 1, 2, 3, . . . ,ε=detuning from quarter-wave retardance, T₀=reference temperature, andλ₀=reference wavelength. With the example parameters selected herein tobe M =0, C_(Verdet)=0.7×10⁻⁴° C.⁻¹ and C_(QW)=−2.4×10⁻⁴° C.⁻¹, thelinear term of the temperature dependence substantially vanishes bysetting ε(T₀,λ₀)=9.5°.

However, a parabolic, i.e. quadratic, term remains which can be foundfrom the equation [13] by Taylor series expansion as follows:

ΔS/S ₀=0.5·ΔT ²·(tan²[ε(T ₀, λ₀)]+sec²[ε(T ₀,λ₀)])·(C _(QW)·[M·180°+90°+ε(T ₀,λ₀)])²   [14]

With the numerical example parameters from above, the quadraticcontribution to AS/S_(o) amounts approximately to 9·10⁻⁸° C.⁻², i.e. to0.033% at 60° C. above or below the reference temperature T₀. In realsensor systems the quadratic signal contribution may exceed this valueas shown in FIG. 10, where it reaches about 0.1% at the extremetemperatures.

This quadratic temperature dependence can be compensated for accordingto the further aspect of the invention. A cross-coupling element 16providing a defined temperature dependent cross-coupling is insertedinto the optical circuit of a fiber-optical sensor, such asfiber-optical current sensor 10 as shown in FIGS. 1, 3A, 3B, 5, and 6 ora fiber-optical-voltage sensor 90 as shown in FIGS. 9A and 9B. Thecross-coupling element is e.g. placed between the polarizing element 2,41, 55 a, 24 a and the sensing element 12 so that the cross-coupling isseparated from the sensing element 12 by at least a retarder 14, aFaraday rotator 14′, or a section of polarization maintaining fiber 11.The disclosed invention can be applied to different embodiments offiber-optic sensors, of which some are described in more detail hereinwith respect to their design and working principle. As thecross-coupling element 16 is preferably exposed to a temperature assimilar as possible to the temperature of the sensing element 12, aconfiguration with element 16 being spatially close to the sensingelement 12, e.g. by sharing a common housing with the sensing element12, is preferred. In other less favourable embodiments the element 16can be a part of the optoelectronic module 10-2, as indicated in FIG.3A.

Temperature-dependent contributions to the signal can—depending on thesensor design—originate from the temperature dependence of themagneto-optic effect in the sensing element 12 (given by the temperaturedependence of the Verdet constant), of the electro-optic effect of thesensing element 12, e.g. given by the temperature dependence of thePockels effect, of the piezo-electric effect of a piezo-electricalmaterial attached to the sensing element, of the intrinsic birefringencein the sensing element 12 such as in a spun highly-birefringent opticalfiber, of bend-induced birefringence in the sensing fiber 12, of theworking point of the sensor, e.g. in a sensor configuration where theworking point is adjusted by a Faraday rotator mirror 15′ (FIG. 6), of afiber retarder at the entrance to the sensing fiber 14, of a Faradayrotator 14′ at the entrance of the sensing element 12 (FIGS. 9a and 9b), of mechanical stress exerted on the sensing fiber, or of combinationsthereof.

For further description, the embodiment of a fiber-optical currentsensor 10 using an optical phase modulator 4 between the polarizingelement 2 and the cross coupling element 16 as in FIG. 3A is consideredin more detail. Nevertheless, the invention can be equally applied todifferent embodiments of fiber-optic sensors, in particular toembodiments with an optical splitter 54 between the polarizing element55 and the cross coupling element 16, with the following mathematicalexpressions and quantitative values being subject to propermodification. Furthermore, it is assumed that the linear temperaturevariation due to the Verdet constant in the sensing fiber 12 iscounteracted by the temperature dependence introduced by the fiberretarder 14 (see equation [13]), i.e. in the numerical example aboveε(τ₀, λ₀) is set to 9.5°. In this case, the quadratic contribution to becompensated by the temperature dependent cross-coupling of element 16amounts to 9×10⁻⁸° C.⁻². In this embodiment, the cross-coupling element16 is represented by an optical retarder 16, preferably a fiber-basedretarder 16 built from a short section of polarization maintainingfiber, with its principal axes aligned under an orientation angle ofwith respect to the incoming light polarization. For example, theretarder 16 can be inserted into the polarization maintaining fibersection 11 as depicted in FIG. 11. Preferably, all polarizationmaintaining fiber sections 11 have a length so that the relative phasedelay exceeds the coherence length of the light source utilized. Withthe retardation of the cross-coupling element 16 denoted by 5, thesignal can be approximately calculated to be

S˜V(T,λ)·NI/(cos[ε(T,λ)]·{cos²[2ζ]+cos[δ(T,λ)]·sin²2ζ})   [15]

Note that by setting ζ=±45°, this expression coincides with theexpression given in equation [3].

Accordingly, by setting the retardance δ(T₀,λ₀) (i.e. half waveretardance or generally retardance of the cross-coupling element 16) toan integer multiple of 180°, the cross coupling element 16 does notintroduce a linear temperature dependence. Under the assumption of avanishing second order temperature dependence of the Verdet constant,the overall second-order temperature dependence then becomes:

ΔS/S ₀=0.5·ΔT ²·{(tan²[ε(T ₀,λ₀)]+sec²[ε(T ₀,λ₀)])·(C _(QW)·[M·180°+90°+ε(T ₀,λ₀)])²+(C_(HW)·δ(T ₀,λ₀))²·cos[δ(T ₀,λ₀)]·sin²[2]/(cos²[2ζ]+cos[δ(T ₀,λ₀)]·sin²[2ζ])}

Accordingly, by setting the retardance δ(T₀,λ₀) of the cross-couplingelement 16 to an odd multiple of 180°, the quadratictemperature-dependent contribution from the cross-coupling element 16 tothe sensor signal counteracts the quadratic temperature-dependentcontribution from the retarder 14 to the sensor signal. Proper choice oforientation angle(s) ζ—depending on the temperature variation ofretardance δ(T₀,λ₀)=m·180° (with m being an odd integer) given byC_(HW)·δ(T₀,λ₀)−results in a vanishing quadratic temperature variation,i.e. together with the temperature compensation by the detunedquarter-wave retarder 14, the sensor signal becomes independent oftemperature up to third order variations in temperature. Overall, theparabolic=quadratic coefficient introduced by the cross-coupling element16 can be tuned by choice of the orientation angle ζ, the order of theretarder m, and the quantity C_(HW). The quantity C_(HW) is given by thetemperature dependence of the birefringence of the optical fiber usedfor the fiber retarder 16 and can accordingly be tuned by the choice ofthe proper type of linear birefringent optical fiber. Typical choicesinclude elliptical core fiber, panda or bow-tie fiber, ellipticalcladding fiber, and microstructured birefringent fiber. With thenumerical parameters from above and assuming C_(HW)=C_(QW), setting m=3and orientation angles ζ=5.25° removes the second order temperaturedependence of the sensor. This is illustrated in FIG. 12, where thecalculated residual quadratic temperature dependence of retarder 14 andsensing element 12 indicated by the dashed curve is counteracted by thecalculated temperature dependence of the cross-coupling element 16indicated by the solid curve such that the combined temperaturedependence of the normalized current signal becomes independent oftemperature (dotted curve).

As seen from expression [16], other choices of retardance δ(T₀,λ₀) andorientation angle of the cross-coupling element 16 yield a differenttemperature dependence of the cross-coupling element 16 that in thegeneral case can also be optimized to compensate a (residual) lineartemperature dependence, e.g. of further components of the fiber-opticalsensor. In particular, in fiber-optic voltage sensors 90, an overalltemperature dependence resulting from the temperature dependence of theelectro-optical effect in the sensing element 12 and of the Faradayrotator 14′ can be compensated for.

In further embodiments of the invention, a first cross-coupling elementcan be used to compensate the overall wavelength dependence of thesensor and a second cross-coupling element can be used to compensate aresidual temperature dependence of the sensor, in particular a quadratictemperature dependence. In such a configuration (not shown), the secondcross-coupling element resides close to the sensing element 12, inparticular in a common housing with the sensing element 12, in order tobe exposed to the same or a similar temperature as the sensing element12; whereas the first-cross coupling preferably shares a common housingwith the opto-electronic module 10-2 or with at least parts of theopto-electronic module 10-2. In configurations where parts of theopto-electronic module 10-2 and the sensing element 12 share a commonhousing, also first and second cross-coupling element can share a commonhousing.

Throughout this application, tan x=sin x/cos x, and sec x=1/cos x, withx being any variable which may also be written in parentheses [x]; andmultiplication can be denoted by dot · or simply by empty space betweenvariables.

While there are shown and described presently preferred embodiments ofthe invention, it is to be understood that the invention is not limitedthereto but may be otherwise variously embodied and practised within thescope of the following claims. In particular, embodiments or featuresrelating to the sensor are also disclosed for the method and vice versa.

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LIST OF REFERENCE SIGNS

light source 1

fiber coupler 101

optical fiber polarizer 2

polarizing splitter 24

45° fiber splice 3

optical phase modulator 4

y-type optical phase modulator, polarizer 41

90° fiber splice 42

polarization maintaining fiber coupler 43

optical delay element 44

detector 5, 5-1, 5-2

integrated optical polarization splitter module 50

spacer 53

splitter 54

polarizer 55 a

polarizer 55 b

polarizer 55 c

quarter-wave retarder 56

signal processor 6

fiber-optical current sensor 10

sensor head 10-1

opto-electronic module 10-2

polarization maintaining fiber 11

sensing element (fiber, crystal) 12

conductor 13

optical retarder 14

Faraday polarization rotator 14′

reflector 15

Faraday polarization rotator mirror 15′

cross-coupling element(retarder, Faraday rotator) 16

fiber sections 16-1, 16-2

temperature stabilized environment 160

magneto-optic material 161

magnet 162

lens(es) 163

optical voltage sensor 90

1-37. (canceled)
 38. A fiber optic sensor comprising: a light source, apolarizing element, a detector, a polarization maintaining (PM) fiber,and a sensing element, wherein the fiber optic sensor further comprisesa cross-coupling element in an optical path between the polarizingelement and the sensing element, with the cross-coupling elementgenerating a defined cross-coupling between the two orthogonalpolarizations of the fundamental mode in the PM fiber, and wherein thecross-coupling element and the sensing element are separated along theoptical path; wherein a quadratically temperature-dependent contributionfrom the cross-coupling element to the sensor signal counteracts aquadratically temperature-dependent contribution from other elements tothe sensor signal.
 39. The fiber optic sensor of claim 38, wherein theother elements comprises a retarder.
 40. The fiber optic sensor of claim38, wherein the cross-coupling element and the sensing element areseparated by at least one element selected from the group consisting of:at least a section of PM fiber, a retarder, a Faraday rotator, andcombinations thereof.
 41. The fiber optic sensor of claim 38, whereinthe cross-coupling element is a separate element present in addition tothe PM fiber.
 42. The fiber optic sensor of claim 41, wherein the PMfiber is a non-ideal PM fiber having residual cross-coupling betweenorthogonal polarizations.
 43. The fiber optic sensor of claim 38,wherein the sensing element is sensitive to an external field selectedfrom an electrical field, a magnetic field or a strain field.
 44. Thefiber optic sensor of claim 38, wherein the cross-coupling elementcomprises an optical retarder or a Faraday rotator.
 45. The fiber opticsensor of claim 38, wherein the cross-coupling element comprises aretarder detuned from exact half-wave retardance or exact multiple-orderhalf-wave retardance by a non-zero amount or phase β(λ_(o)).
 46. Thefiber optic sensor of claim 38, wherein the cross-coupling element is afiber retarder comprising a birefringent fiber, an elliptical core fiberor a microstructured birefringent fiber.
 47. The fiber optic sensor ofclaim 38, wherein the principal optical axes of the PM fiber and theprincipal optical axes of the cross-coupling element are rotated againsteach other by an orientation angle in the range of ±(45°±22.5°).
 48. Thefiber optic sensor of claim 38, wherein the principal optical axes ofthe PM fiber and the principal optical axes of the cross-couplingelement are rotated against each other by an orientation angle ζ in therange of ±(45°±10°).
 49. The fiber optic sensor of claim 38, wherein thecross-coupling element is a half wave retarder with principal axesforming an orientation angle ζ in the range of ±15° or in a range of90°±15° with respect to the principal axes of the PM fiber, and with ahalf wave retardance δ(T₀,λ₀) equal to an integer multiple of 180°within ±20° to achieve a sensor signal insensitive to temperature up tosecond order within a given temperature range.
 50. The fiber opticsensor of claim 38, comprising a retarder adjusted to compensate forlinearly temperature-dependent shifts in the sensor signal caused bytemperature changes of any of the elements selected from the groupconsisting of: the cross-coupling element, the sensing element, andfurther optical elements in the fiber optic sensor.
 51. The fiber opticsensor of claim 50, wherein the retarder introduces a quadraticallytemperature-dependent shift in the sensor signal.
 52. The fiber opticsensor of claim 38, wherein the sensing element comprises a sensingfiber to be looped around a conductor and to be in operation exposed toa magnetic field of a current I in the conductor.
 53. The fiber opticsensor of claim 38, wherein the sensing element comprises anelectro-optical crystal or an electro-optic fiber or a fiber connectedto piezo-electric material.
 54. The fiber optic sensor of claim 38,wherein the sensing element is terminated with a reflective element. 55.The fiber optic sensor of claim 38, wherein the optical path with thecross-coupling element comprises an optical phase modulator between thepolarizing element and the sensing element.
 56. The fiber optic sensorof claim 38, wherein the optical path with the cross-coupling elementcomprises an optical beam splitter between the polarizing element andthe sensing element.
 57. A high-voltage power transmission networkcomprising the fiber optic sensor of claim 38.